In mathematics, the classifying space for the orthogonal group O(n) may be constructed as the Grassmannian of n-planes in an infinite-dimensional real space .
The cohomology ring of with coefficients in the field of two elements is generated by the Stiefel–Whitney classes: [1] [2]
The canonical inclusions induce canonical inclusions on their respective classifying spaces. Their respective colimits are denoted as:
is indeed the classifying space of .
In mathematics, the classifying space for the orthogonal group O(n) may be constructed as the Grassmannian of n-planes in an infinite-dimensional real space .
The cohomology ring of with coefficients in the field of two elements is generated by the Stiefel–Whitney classes: [1] [2]
The canonical inclusions induce canonical inclusions on their respective classifying spaces. Their respective colimits are denoted as:
is indeed the classifying space of .